Electron Cyclotron Resonance in Plasmas

For higher pressures, very little resonance is seen as electron collisions occur so frequently that the electron cannot be turned by the magnetic field in time to catch the reversing electric field. At lower pressures, there is a strong resonance. 

The behavior of such a resonant discharge can be described by solving the continuum momentum equations for electron velocity, assuming a constant frequency ve. The force on the electrons is both due to the electric field and the Lorentz force caused by the magnetic field. The average power input per unit volume to the plasma is found to be10 

It is useful to compare this power input to a plasma to the power that would be input when no magnetic field is present (we = 0). Then we can write 

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